With the promise to shape the future of industry, multi-agent robotic technologies have the potential to change many aspects of daily life. Over the coming decade, they are expected to impact transportation systems, military applications such as reconnaissance and surveillance, search-and-rescue operations, or space missions, as well as provide support to emergency first responders. Motivated by the latest developments in the field of robotics, this thesis contributes to the evolution of the future generation of multi-agent robotic systems as they become smarter, more accurate, and diversified in terms of applications. But in order to achieve these goals, the individual agents forming cooperative robotic systems need to be specialized in what they can accomplish, while ensuring accuracy and preserving the ability to perform diverse tasks. This thesis addresses the problem of task allocation in swarm robotics in the specific context where specialized capabilities of the individual agents are considered. Based on the assumption that each individual agent possesses specialized functional capabilities and that the expected tasks, which are distributed in the surrounding environment, impose specific requirements, the proposed task allocation mechanisms are formulated in two different spaces. First, a rudimentary form of the team members’ specialization is formulated as a cooperative control problem embedded in the agents’ dynamics control space. Second, an advanced formulation of agents’ specialization is defined to estimate the individual agents’ task allocation probabilities in a dedicated specialization space, which represents the core contribution of this thesis to the advancement and practice in the area of swarm robotics. The original task allocation process formulated in the specialization space evolves through four stages of development. First, a task features recognition stage is conceptually introduced to leverage the output of a sensing layer embedded in robotic agents to drive the proposed task allocation scheme. Second, a matching scheme is developed to best match each agent’s specialized capabilities with the corresponding detected tasks. At this stage, a general binary definition of agents’ specialization serves as the basis for task-agent association. Third, the task-agent matching scheme is expanded to an innovative probabilistic specialty-based task-agent allocation framework to generalize the concept and exploit the potential of agents’ specialization consideration. Fourth, the general framework is further refined with a modulated definition of the agents’ specialization based on their mechanical, physical structure, and embedded resources. The original framework is extended and a prioritization layer is also introduced to improve the system’s response to complex tasks that are characterized based on the recognition of multiple classes. Experimental validation of the proposed specialty-based task allocation approach is conducted in simulation and on real-world experiments, and the results are presented and discussed in light of potential applications to demonstrate the effectiveness and efficiency of the proposed framework.